What are the initial position vector →ri and final position vector →rf, both in unit-vector notation? What is the x component of displacement Δ→r?
(i)
Position vector →ri
(x)
5^i−3^j−1^k
(ii)
Postion vector →rf
(y)
−2^i−4^j+1^k
(iii)
x-component of displacement Δ→r
(z)
7^i+1^j−2^k
What are the initial position vector →ri and final position vector →rf, both in unit-vector notation? What is the x component of displacement Δ→r?
| (i) | Position vector →ri | (x) | 5^i−3^j−1^k |
| (ii) | Postion vector →rf | (y) | −2^i−4^j+1^k |
| (iii) | x-component of displacement Δ→r | (z) | 7^i+1^j−2^k |
The correct option is B (i) - (z); (ii) - (x); (iii) - (y)
By looking at the picture, I can say to reach i from 0, I have walked 7m on the x-axis, 1m on the y-axis and 2m on the -ve z-axis.
So my ri=7^i+1^j−2^k, similarly rf=5^i−3^j−1^k. Now displacement vector is →rf−→ri=Δ→r
⇒(5^i−3^j−1^k)−(7^i+1^j−2^k)
⇒△→r=−2^i−4^j+1^k
This means to reach point 'f' from i we have to walk 2m in the -ve x-axis then 4m on -ve y-axis and then 1m on +ve axis so x-component or the displacement along the positive direction of x-axis is -2m.
(i) - (z); (ii) - (x); (iii) - (y)
By looking at the picture, I can say to reach i from 0, I have walked 7m on the x-axis, 1m on the y-axis and 2m on the -ve z-axis.
So my ri=7^i+1^j−2^k, similarly rf=5^i−3^j−1^k. Now displacement vector is →rf−→ri=Δ→r
⇒(5^i−3^j−1^k)−(7^i+1^j−2^k)
⇒△→r=−2^i−4^j+1^k
This means to reach point 'f' from i we have to walk 2m in the -ve x-axis then 4m on -ve y-axis and then 1m on +ve axis so x-component or the displacement along the positive direction of x-axis is -2m.
